DFT Studies on Substituent Effects in Palladium-Catalyzed Olefin

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Organometallics 2000, 19, 1850-1858

DFT Studies on Substituent Effects in Palladium-Catalyzed Olefin Polymerization Artur Michalak†,‡ and Tom Ziegler*,† Department of Chemistry, University of Calgary, University Drive 2500, Calgary, Alberta, Canada T2N 1N4, and Department of Theoretical Chemistry, Jagiellonian University, R. Ingardena 3, 30-060 Cracow, Poland Received November 17, 1999

Gradient-corrected density functional theory has been used to study substituents effects on the cationic N∧N-Pd(II) diimine catalyst in ethene and propene polymerization. Here N∧N ) -C(R)-N(Ar)-N(Ar)-C(R)- with R ) H, -CH3, -An and Ar ) H, C6H5, -2,6-C6H3(Me)2, -2,6-C6H3(iPr)2. Calculations have been performed on the [N∧N-Pd(II)-P]+ (P ) n-propyl and isopropyl) alkyl complexes (1) and the corresponding [N∧N-Pd(II)-P(η2-CH2CHRo)]+ π-complexes of ethene (Ro ) H) and propene (Ro ) CH3), as well as the ethene and propene (1,2- and 2,1-) insertion transition states. The results show that an increase in the size of the substituents on the Pd(II) catalyst enhances the preference of 1 for the isomer with the branched isopropyl alkyl group P, while for the olefin complexes [N∧N-Pd(II)-P(η2CH2CHRo)]+ the isomer with the linear n-propyl group P becomes preferred. Further, an increase in the size of the substituents affects the relative binding of ethene and propene. Thus, the electronic preference of propene complexes is overridden by steric factors in the case of the largest substituents. The regioselectivity of propene insertion is strongly affected as well: an increase in steric demand decreases the 2,1-:1,2-insertion ratio, with 1,2-insertion becoming favored for the sterically most congested catalyst [R ) -CH3, Ar ) -2,6C6H3(iPr)2]. Introduction The Ni(II) and Pd(II) complexes with diimine ligands introduced by Brookhart and co-workers1-4 were among the first examples of late-transition-metal-based catalyst capable of polymerizing ethene and R-olefins to high molecular weight polymers. The Pd-based catalysts were also among the first to copolymerize R-olefins with monomers containing polar groups such as acrylates and vinyl ketones.3,4 As for other transition-metal-based olefin polymerization catalysts,5,6 changes in the reaction conditions and modifications of the coligands on the catalyst can potentially control the properties of the resulting polymers, including their microstructure.7 Therefore, it is important to understand how changes of the catalyst substituents affect the elementary reactions of the polymerization processes. The R-olefins polymerization mechanism is shown in Scheme 1. In the case of the Brookhart catalyst, the resting state is an olefin π-complex,1 A, from which the †

University of Calgary. Jagiellonian University. (1) Johnson, L. K.; Killian, C. M.; Brookhart, M J. Am. Chem. Soc. 1995, 117, 6414. (2) Killian, C. M.; Tempel, D. J.; Johnson, L. K.; Brookhart, M. J. Am. Chem. Soc. 1996, 118, 11664. (3) Johnson, L. K.; Mecking, S.; Brookhart, M. J. Am. Chem. Soc. 1996, 118, 267. (4) Mecking, S.; Johnson, L. K.; Wang, L.; Brookhart, M. J. Am. Chem. Soc. 1998, 120, 888. (5) Britovsek, G. J. P.; Gibson, V. C.; Wass, D. F. Angew. Chem., Int. Ed. 1999, 38, 428. (6) Brintzinger, H.; Fischer, D.; Mulhaupt, R.; Rieger, B.; Waymouth, R. M. Angew. Chem., Int. Ed. Engl. 1995, 34, 1143. (7) Guan, Z.; Cotts, P. M.; McCord, E. F.; McLain, S. J. Science 1999, 283, 2059. ‡

polymer chain may grow via two alternative insertion paths. The 1,2-insertion (reaction RA) gives rise to a β-agostic alkyl complex B with the unsubstituted olefin carbon attached to the metal. On the other hand, the 2,1-insertion (reaction RB) leads to the formation of the complex C with the substituted olefin carbon linked to the metal. Both insertion reactions introduce the branch Ro prior to the formation of new π-complexes by olefin uptake. However, prior to the olefin uptake and subsequent insertion the polymer chain may isomerize via reactions RC and RD, resulting in the complexes A and D, where tertiary and primary carbon atoms are forming bonds with the palladium metal, respectively. The isomerization reaction (RC) introduces an additional methyl branch, while the chain straightening isomerization reaction (RD) shortens and eventually removes a branch, leading to the linear polymer chain. Obviously, in the ethene case with Ro ) H the two insertion paths are indistinguishable. Thus, the insertion leads to the linear polymer, and the isomerization reaction (RC) is responsible for branching of the polymer. It has been observed experimentally1-4,7 that polyethylene materials obtained with the Brookhart catalysts have a relatively high number of branches, while in the case of higher R-olefins the number of branches is much lower than that expected from regular, subsequent insertions. Moreover, not only the number of branches but also their microstructure7 can be controlled by changes in reaction conditions and the catalyst structure. In a previous study8 we reported a detailed analysis of the elementary steps in the Pd-catalyzed propene and (8) Michalak, A.; Ziegler, T. Organometallics 1999, 18, 3998.

10.1021/om990910t CCC: $19.00 © 2000 American Chemical Society Publication on Web 04/07/2000

Pd-Catalyzed Olefin Polymerization

Organometallics, Vol. 19, No. 10, 2000 1851

Scheme 1. Elementary Reaction Steps in Pd(II)-Catalyzed Olefin Polymerization

ethene polymerization processes with the catalyst modeled by a generic system in which diimine substituents were replaced by hydrogen atoms. In the present study we will present the results of our theoretical investigation of ethene and propene polymerization by a Pd-based diimine catalyst with a variety of substituents. We will discuss the effect of substituents on the regioselectivity of propene insertion, propene and ethene insertion barriers, and relative stabilities of alkyl and olefin complexes containing alkyl chains with primary and secondary carbon atom attached to the metal. We will also discuss the influence of substituents on the relative stabilities of ethene and propene π-complexes. In the computational studies on steric effects in large molecular systems, the hybrid quantum chemical molecular mechanics (QM/MM) approaches are often applied. They can be used to roughly estimate the influence of steric factors within the accuracy of a few kcal/ mol. In the present studies we compare the complexes in which the steric effects are not dramatically different. As will be demonstrated in the paper, some of the energy differences obtained from the present studies are already at the edge of the QM-DFT accuracy and below the accuracy of QMMM methods. Therefore, we decided to treat all the systems discussed here with complete quantum mechanical calculations at the level of nonlocal density functional theory (DFT) and not to apply the QMMM methodology. Other aspects of ethylene polymerization by Brookhart Ni- and Pd-catalysts, which we do not intend to discuss here, were the subject of recent theoretical studies.9-16 Thus, effects of bulky diimine substituents on the termination, isomerization, and insertion barriers, as well as the olefin capture, were studied by static and (9) Margl, P.; Deng, L.; Ziegler, T. J. Am. Chem. Soc. 1999, 121, 154. (10) Deng, L.; Margl, P.; Ziegler, T. J. Am. Chem. Soc. 1997, 119, 1094. (11) Deng L.; Woo, T. K.; Cavallo, L.; Margl, P M.; Ziegler T. J. Am. Chem. Soc. 1997, 119, 6177. (12) Woo, T. K.; Blochl, P. E.; Ziegler, T J. Phys. Chem. A 2000, 104, 121. (13) Woo, T. K.; Ziegler, T. J. Organomet. Chem., in press. (14) Musaev, D. G.; Svensson, M.; Morokuma, K.; Stro¨mberg, S.; Zetterberg, K.; Siegbahn, P. E. M. Organometallics 1997, 16, 1933. (15) Froese, R. D. J.; Musaev, D. G.; Morokuma, K. J. Am. Chem. Soc. 1998, 120, 1581. (16) Musaev, D. G.; Froese, R. D. J.; Morokuma, K. Organometallics 1998, 17, 1850.

dynamic hybrid, quantum chemical molecular mechanics (QMMM) methods with a molecular mechanics representation of the substituents. Computational Details and the Model Systems All the results were obtained from DFT calculations with the Becke-Perdew exchange-correlation functional,17-19 using the Amsterdam Density Functional (ADF) program.20-25 For the Pd atom the standard triple-ζ STO basis set (from ADF database IV) was employed, with 1s-3d electrons treated as a frozen core. For the other elements the standard double-ζ STO basis sets with one set of polarization functions (from ADF database III) were applied, with frozen cores including 1s electrons for C and N.26,27 The auxiliary28 s, p, d, f, and g STO functions centered on all nuclei were used to fit the Coulomb and exchange potentials during the SCF process. The reported relative energies include first-order relativistic correction,29-31 since it was shown that such an approach is sufficient for the systems containing the 4d transition metals.32 Scheme 2 displays the different diimine ligands (N∧N ) -N(Ar)-C(R)-C(R)-N(Ar)-) considered in this work. A total of nine combinations were studied, corresponding to backbone substituents R ) H, -CH3, -C10H6 (R ≡ An) and Ar ) H, -C6H5, -2,6-C6H3(Me)2, -2,6-C6H3(iPr) (a-i of Scheme 2). The number of possible alkyl [N∧N-Pd(II)-P]+ (N∧N ) a-i; P) (17) Becke, A. Phys. Rev. A 1988, 38, 3098. (18) Perdew, J. P. Phys. Rev. B 1986, 34, 7406. (19) Perdew, J. P. Phys. Rev. B 1986, 33, 8822. (20) Baerends, E. J. Ph.D. Thesis, Free University, Amsterdam, The Netherlands, 1973. (21) Baerends, E. J.; Ellis, D. E.; Ros, P. Chem. Phys. 1973, 2, 41. (22) Ravenek, W. In Algorithms and Applications on Vector and Parallel Computers; te Riele, H. J. J., Dekker, T. J., van de Horst, H. A., Eds.; Elsevier: Amsterdam, The Netherlands, 1987. (23) te Velde, G.; Baerends, E. J. J. Comput. Chem. 1992, 99, 84. (24) Boerrigter, P. M.; te Velde, G.; Baerends, E. J. Int. J. Quantum Chem. 1988, 33, 87. (25) Versluis, L.; Ziegler, T. J. Chem. Phys. 1988, 88, 322. (26) Snijders, J. G.; Baerends, E. J.; Vernoijs, P. At. Nucl. Data Tables 1982, 26, 483. (27) Vernoijs, P.; Snijders, J. G.; Baerends, E. J. Slater Type Basis Functions for the Whole Periodic System; Internal report (in Dutch); Department of Theoretical Chemistry, Free University: Amsterdam, The Netherlands, 1981. (28) Krijn, J.; Baerends, E. J. Fit Functions in the HFS Method; Internal Report (in Dutch); Department of Theoretical Chemistry, Free University: Amsterdam, The Netherlands, 1984. (29) Ziegler, T.; Tschinke, V.; Baerends, E. J.; Snijders, J. G.; Ravenek, W. J. Phys. Chem. 1989, 93, 3050. (30) Snijders, J. G.; Baerends, E. J. Mol. Phys. 1978, 36, 1789. (31) Snijders, J. G.; Baerends, E. J.; Ros, P. Mol. Phys. 1979, 38, 1909. (32) Deng, L.; Ziegler, T.; Woo, T. K.; Margl, P.; Fan, T. Organometallics 1998, 17, 3240.

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Michalak and Ziegler

Scheme 2. Scope of Investigated Alkyl and Olefin Complexes

Table 1. Relative Stabilities of Isomer Complexes Alkyl β-Agostic and Olefin π-Complexes relative energiesa catalyst x

R

Ar

alkyl complexes (β-agostic) E(1′x)b - E(1x)c

a b c d e f g h i

H H H H CH3 CH3 CH3 An An

H C6H5 2,6-C6H3Me2 2,6-C6H3iPr2 H 2,6-C6H3Me2 2,6-C6H3iPr2 H 2,6-C6H3iPr2

-1.96 -2.47 -3.11 -3.21 -1.75 -2.76 -2.36 -1.87 -2.65

ethene π-complexes E(2′x)b - E(2x)c

propene π-complexes E(4′x)b - E(4x)c

-1.32 +1.62 +0.71 +1.24 -0.70 +1.96 +3.28 -1.45 +2.01

-1.20 +1.97 +1.28 +1.50 -1.02 +2.15 +3.31 -1.14 +1.94

a Energy differences between corresponding complexes with isopropyl and n-propyl alkyls; in kcal/mol. b Species indicated by a prime contain the isopropyl group, see Scheme 2. c Species indicated without a prime contain the n-propyl group, see Scheme 2.

n- and isopropyl) and olefin complexes [N∧N-Pd(II)-P(η2CH2CHRo)]+ (N∧N ) a-i; P ) n- and isopropyl; Ro ) H, Me) is considerable. Here we shall constrain our calculations to the most important reaction intermediates only; see Scheme 2. The systems considered are (i) the alkyl β-agostic complexes with n-propyl (1a-i) and isopropyl (1′a-i) groups as models for the polymer chain; (ii) ethene π-complexes with n-propyl (2a-i) and isopropyl alkyl (2′a-i); (iii) ethene insertion transition states, with n-propyl alkyl (3a-i); (iv) propene π-complexes with n-propyl (4a-i) and isopropyl (4′a-i) alkyl; (v) propene 1,2- (5a-i) and 2,1- (6a-i) insertion transition states, with n-propyl alkyl. The above set of complexes allows us to discuss the influence of the catalyst substituents on the relative stability of isomeric alkyl complexes, the stabilization of isomeric ethene and propene π-complexes, ethene and propene insertion barriers, and the propene 1,2-:2,1-insertion ratio. A complete analysis of the ethene and propene polymerization mechanism for the generic catalyst model (R ) H, Ar ) H) was presented in our previous paper.8

Results and Discussion A. Relative Stability of the Isomer Alkyl Complexes. The energy differences between the isopropyl and n-propyl β-agostic complexes are listed in the first column of Table 1. It can be seen that the isopropyl

systems are more stable, by 1.5-3.2 kcal/mol, for all catalyst models. Further, the relative energy of the two alkyl isomers is only slightly influenced by changes in the backbone substituents (compare entries a, e, and h). On the other hand an increase in the size of Ar has a more pronounced effect, leading to enhanced preference for the branched isomer. In the previous paper8 we showed for a generic system (R ) H, Ar ) H) that the relative stability of the isomeric alkyl complexes is determined by two main factors: the relative stability of alkyl radicals and the catalyst-alkyl bonding energy comprising both Pd-C and Pd-H agostic bond formation. We demonstrated8 further that with a change in alkyl group, these two factors change in opposite directions: the more branched alkyl is more stable than the less branched one, but at the same time the more branched alkyl is more weakly bonded. As a result, the relative stability of the isomeric β-agostic alkyl complexes resembles that of the corresponding alkyl radicals, albeit with a lower energy difference between a given pair of complexes. In the case of the real systems, since the introduction of large Ar groups results in an increase in steric repulsion between the diimine ligand and any alkyl group, this leads to a Pd-alkyl bond weakening. As a result, the energy


Organometallics, Vol. 19, No. 10, 2000 1853 Table 3. Values of Torsional Angles Describing Rotation of Aryl Rings in Alkyl β-Agostic Complexesa torsional angle catalyst R

Ar

H H H CH3 CH3 An

C6H5 2,6-C6H3Me2 2,6-C6H3iPr2 2,6-C6H3Me2 2,6-C6H3iPr2 2,6-C6H3iPr2

a

primary alkyl 1b 1c 1d 1f 1g 1i

φ1

φ2

42.5 73.5 66.5 84.3 77.9 85.6

32.8 53.5 54.7 109.7 77.4 79.9

secondary alkyl 1′b 1′c 1′d 1′f 1′g 1′i

φ1

φ2

46.8 75.7 66.7 80.8 73.7 85.2

32.7 51.3 54.8 70.17 70.12 74.8

See Figure 2a for definition of angles.

Figure 1. Analysis of factors important for the relative stability of isomeric alkyl complexes (a). Relative energy (schematic) of the two alkyl radicals (column 1) as well as the “real” and “generic” alkyl complexes (columns 2 and 3). (b) Pd-alkyl bonding energies in the “real” and “generic” alkyl complexes (columns 2 and 3). Generic system represented by R ) H, Ar ) H. Table 2. Pd-C and Pd-H Bond Lengths in β-Agostic Alkyl Complexes bond lengthsa catalyst R

Ar



primary alkylc 1a 1b 1c 1d 1e 1f 1g 1h 1i

Pd-C

Pd-H

2.065 2.067 2.069 2.070 2.064 2.067 2.070 2.06 2.068

1.787 1.794 1.820 1.830 1.782 1.809 1.814 1.78 1.810

secondary alkylb 1′a 1′b 1′c 1′d 1′e 1′f 1′g 1′h 1′i

Pd-C

Pd-H

2.079 2.077 2.080 2.079 2.076 2.085 2.083 2.07 2.082

1.815 1.825 1.852 1.855 1.805 1.840 1.824 1.81 1.848

a

In angstroms. b Species indicated by a prime contain the isopropyl group, see Scheme 2. c Species indicated without a prime contain the n-propyl group, see Scheme 2.

differences between the isomers are increased (the alkyl radical stability plays a more important role) in comparison to the complexes with a generic catalyst. We have illustrated this qualitatively in Figure 1. The changes in the Pd-alkyl bonding energy with the steric bulk of the diimine substituents are reflected in the Pd-C and, mainly, the Pd-H bond lengths, collected in Table 2. Indeed, these data correlate with the relative energies of Table 1: the shortest interatomic distances for catalyst h (R ) An, Ar ) H) correspond to the lowest energetic preference of the complex with a branched alkyl, while the longest Pd-C and Pd-H bonds in the case of complexes 1d and 1′d are accompanied by the largest preference of the isopropyl system. For all the remaining, intermediate cases, the alkyl-catalyst bond weakening/strengthening corresponds to an increase/decrease in the energetic preference of the complex with a secondary alkyl. It may seem quite surprising, however, that the weakening of the catalyst-alkyl bonds is larger for the systems with R ) H than for those with R ) CH3 or

Figure 2. Definition of torsional angles φ1 and φ2 describing rotation of the aryl rings around N-C bonds in alkyl β-agostic (panel a) and olefin π-complexes (panel b). A value of 90° corresponds to perpendicular orientation of an aryl ring with respect to the Pd-N-N-C-C ring.

An. It can be partially attributed to the electronic effect of R: for the systems e and h (R ) CH3, An, respectively; Ar ) H) we observe the strengthening of both the Pd-C and the Pd-H bonds, in comparison to the system a (R ) H, Ar ) H), as reflected by the bond lengths of Table 2 and the relative energies of Table 1. Also, it is important here that an introduction of backbone substituents affects the orientation of the catalyst phenyl rings. In Table 3 we collected the torsional angles that characterize the phenyl ring rotation around the N-C bonds, as defined in Figure 2a. One can see that the electronic preference of the planar orientation of all three rings (two aryls and PdN2C2) to increase the conjugation of the π-electron systems is overridden by steric effects. The repulsion between the backbone hydrogens and the Ar group enforces the more vertical (closer to perpendicular) orientation of both aryl rings for the catalyst c in comparison to b. However, when the size of the aryl ortho substituents is dramatically increased in the system d, yet another effect plays an important role, namely, the repulsion between the substituents of the two aryl rings. As a result of the latter interactions, the orientation of the rings in the catalyst d is less vertical than in the system c, where the repulsion between the two methyl groups on differ-

1854


ent aryls is less important than the repulsion between the aryl methyls and the backbone hydrogens. A similar effect is observed for the systems f and g, when the methyl group is introduced as R, and in the system i (R ) An). Obviously, since the repulsion between the aryl groups and the backbone methyls is larger than in the case of backbone hydrogens, the rings in the cases f and g or i are more vertically oriented than in c and d, respectively. Eventually, as a result of the less vertical ring orientation for R ) H, the repulsion between the aryl substituents and the alkyl group is increased, and the alkyl-catalyst bonds are weakened more then in the systems with R ) CH3, An. Finally, it is interesting to compare our results with those obtained from QM/MM approaches for the catalyst f (R ) -CH3, and Ar ) -2,6-C6H3(iPr)2) and the Nibased catalyst with the same ligands. In all these cases QM/MM methods predicted an opposite substituent effect, i.e., preference of the linear isomer in the case of real catalyst (by ca. 0.5 kcal/mol11 or 6.5 kcal/mol15 for Ni-based catalyst and 0.5 kcal/mol15 for Pd-based catalyst). Most likely, this is due to an overestimation of the steric repulsion in the isopropyl case (leading to its destabilization in comparison to the n-propyl complex). It can be observed that the Pd-C bond lengthening in the isopropyl system with the real catalyst is larger in the QM/MM15 (0.011 Å) than in our studies (0.005 Å), while for the n-propyl systems the QM/MM and our results are closer (by 0.005 Å in QMMM and by 0.007 Å in the present studies). To conclude this part of the discussion, we would like to point out that despite small irregularities in the trend, the general effect observed in all the real systems is an enhanced preference of the branched isomer. Thus, the chain straightening isomerization reaction (RD in Scheme 1) becomes even less facile in the real systems. However, as we emphasized in our previous study,8 to explain the branching in polyolefins, additional factors due to olefin coordination must be taken into account. We shall discuss them in the following sections. B. Relative Stability of Isomeric Olefin π-Complexes. In the last two columns of Table 1 we list the energy differences between olefin π-complexes with the iso- and n-propyl alkyl groups, for ethene and propene. One can observe that for all the real catalysts (Ar > H) the n-propyl isomer is strongly preferred (by 1.3-3.3 kcal/mol); that is, the preference of the branched isomer observed in the generic systems (Ar ) H) has been reversed. Moreover, the effect of the size of the aryl substituents is clear and regular: the larger the substituents are, the more favored is the linear isomer. This is true for all backbone substituents (R ) H, CH3, An). Also, the electronic effect of R leads to the preference of the respective n-propyl systems; for the catalysts e and h (R ) CH3, An; Ar ) H) one can see a decrease in the energy difference between the two isomers in comparison to the system a (R ) H, Ar ) H). The preference of the isomer with a linear alkyl can be easily explained by steric interactions between the alkyl chain and the aryl substituents of the diimine ligand. Namely, while in the n-propyl case there exists a repulsion between one aryl substituent and the alkyl, in the isopropyl isomer similar interactions are present between both alkyl methyls and both aryl substituents.


This is shown schematically in Figure 3a. Moreover, in the n-propyl complexes the steric repulsion between the alkyl chain and the aryl substituents can in part be reduced by aryl rotation, which increases the distance between the two interacting groups. In the isopropyl complexes this is impossible since increasing the distance between the two groups by aryl rotation results in a decrease of the distance between the two groups of the other pair. In Table 4 we have collected values of the angles that describe rotation of the aryl groups (see Figure 2b). The values of the angle φ1 show that in the case of isopropyl complexes the orientation of the aryl rings is always closer to perpendicular than in n-propyl complexes. Obviously, this increased steric repulsion in the real systems with a branched alkyl is present in the complexes involving any olefin. Therefore, a similar trend in the relative stabilities of isomers can be observed for ethene and propene complexes. Indeed, the numbers presented in Table 1 show that there are only small differences between the two olefins with this respect. One can expect, however, that the change of olefin will affect the π-complex stabilization energies. Finally, we would like to point out that the isomeric olefin π-complexes are relatively close in energy, so are the alkyl agostic complexes discussed in the previous section. Moreover, the energy differences between isomers do not change significantly with a change of catalyst substituents. This could be of concern for the validity of the present study, since it is known that small energy differences can be reversed when changing the level of calculations. However, the trends observed in the series of catalyst models are quite regular, consistent with the calculated changes in the molecular geometries, and easy to explain on the basis of the electronic and steric factors. Therefore, we believe that the choice of the NL-DFT with the Becke-Perdew exchange-correlation functional is justified in this case, and the results presented in the present article are correct. C. Olefin π-Complex Stabilization. In Table 5 the ethene and propene π-complex stabilization energies for the complexes with primary and secondary alkyl (npropyl and isopropyl) are presented. The relative energies of Table 5 have been calculated with respect to the energies of separated reactants, i.e., free olefin and the β-agostic alkyl complex. Therefore, they reflect both effects discussed previously: an enhanced preference of branched alkyl complex, and the olefin complex with linear alkyl in the systems comprising diimine ligands with large substituents. As a result, this leads to a substantial decrease in stabilization energies for the complexes with a secondary alkyl, in comparison to those with a primary one. We have schematically illustrated this in Figure 4. The results presented in Table 4 show that this effect is similar for both olefins; one can observe the increase in the difference in the stabilization energies for the two isomeric complexes, from 0.64 and 0.77 kcal/mol in the generic systems (2a, 2′a; 4a, 4′a) up to 5.63 and 5.66 kcal/mol in the complexes with R ) H and Ar ) C6H3(iPr)2, for ethene and propene, respectively. To further examine the role of steric and electronic factors in the π-complex stabilization energies, we present in Table 6 a fragment



Figure 3. Steric and electronic preferences in olefin π-complexes with branched and linear alkyl groups. (a) Steric and electronic preferences of isopropyl vs n-propyl. (b) Steric and electronic preferences of propene vs ethene π-complexes. (c) 2,1- vs 1,2-insertion of propene. Table 4. Values of Torsional Angles Describing Rotation of Aryl Rings in Olefin π-Complexesa torsional angle catalyst

primary alkyl

secondary alkyl

R

Ar

ethene

φ1, φ2

propene

φ1, φ2

ethene

φ1, φ2

propene

φ1, φ2

H H H CH3 CH3 An

C6H5 2,6-C6H3Me2 2,6-C6H3iPr2 2,6-C6H3Me2 2,6-C6H3iPr2 2,6-C6H3iPr2

2b 2c 2d 2f 2g 2i

54.6, 46.0 71.1, 56.7 67.3, 58.2 79.2, 75.1 75.0, 72.3 87.6, 71.6

4b 4c 4d 4f 4g 4i

53.4, 47.5 69.0, 60.3 66.9, 60.0 78.9, 75.6 75.4, 73.7 88.3, 74.0

2′b 2′c 2′d 2′f 2′g 2′i

118.1,38.8 91.4, 58.1 84.1, 56.1 84.7, 81.6 77.0, 77.7 89.2, 74.0

4′b 4′c 4′d 4′f 4′g 4′i

118.1, 38.9 84.8, 59.3 83.2, 58.1 84.5, 82.7 77.4, 79.3 88.6, 76.8

a

See Figure 2a for definition of angles.

analysis of the stabilization energies presented in Table 5. In this analyses, the olefin complexation energy is decomposed as

∆E ) ∆Eg + ∆Eb ) (∆Eo + ∆Ec ) + ∆Eb

(1)

where ∆Eg ) ∆Eo + ∆Ec is a reactants geometry distortion term, comprising distortions of olefin (∆Eo; with respect to the free olefin geometry) and of the alkyl

complex (∆Ec, with respect to the alkyl β-agostic complex), while ∆Eb describes the binding energy calculated with respect to the distorted reactants. The influence of the steric factors can be clearly seen by comparing results from generic and real systems. Thus, for the generic model the catalyst distortion energies are much smaller for the complexes with isopropyl compared to n-propyl. This is mainly dictated by the required break-

1856



Table 5. Olefin π-Complex Stabilization Energies relative energiesa catalyst

primary alkyl

R

Ar



a

ethene 2a 2b 2c 2d 2e 2f 2g 2h 2i

-18.82 -17.75 -19.72 -18.91 -18.86 -19.71 -16.44 -19.37 -19.14

secondary alkyl propene

4a 4b 4c 4d 4e 4f 4g 4h 4i

-20.85 -19.69 -21.25 -20.48 -20.22 -20.88 -16.34 -21.03 -16.82

ethene 2′a 2′b 2′c 2′d 2′e 2′f 2′g 2′h 2′i

-18.18 -13.68 -15.89 -14.46 -17.80 -15.00 -10.81 -18.96 -14.49

propene 4′a 4′b 4′c 4′d 4′e 4′f 4′g 4′h 4′i

-20.08 -15.23 -16.86 -15.78 -19.48 -15.97 -10.68 -20.30 -12.23

With respect to the energy of isolated reactants, i.e., free olefin and alkyl β-agostic complexes; in kcal/mol.

Figure 4. Relative energies of isomer β-agostic and olefin π-complexes in generic (R ) H, Ar ) H) and real systems (Ar > H) relative to n-propyl agostic complexes. In the real systems with an isopropyl alkyl, the huge decrease in π-complex stabilization energy ∆Eiso-Pr in comparison to ∆En-Pr comes as a result of two factors: decreased stability of the π-complex and increased stablity of the mother agostic complexes.

ing of the β-agostic bond, which is stronger in the n-propyl case. For all the real systems (Ar > H), however, ∆Ec becomes much larger in the isopropyl case, as a result of the repulsion between the alkyl chain and the aryl substituents in the π-complex geometry (see Figure 3b). The corresponding increase in the olefin distortion energies for the isopropyl complexes is much smaller. Also, from the results of Table 6 it can be seen that the difference in ∆Eb for the two alkyl isomers remains almost constant with a change of aryl substituents (ca. 2-2.5 kcal/mol); that is, for both alkyls an increase in the size of the substituents results in a similar weakening of the bond between olefin and catalyst, already distorted. The results of Table 5 show that for the systems involving the most bulky substituents on the diimine ligand, g and i, the ethene π-complexes are stabilized more strongly than the propene ones. In the previous generic study8 we showed that larger stabilization of propene π-complexes in a generic system (a) comes from the higher energy of the propene HOMO orbital, which facilitates the olefin f catalyst charge transfer. Here we see that this electronic preference is overridden by steric factors in the systems with large substituents. We qualitatively explain this in Figure 3b: in the propene case the increased steric repulsion between the methyl group and an aryl substituent destabilizes the π-complex. The preference of ethene π-complexation for the

real catalysts is in agreement with the experimental data: it has been observed that ethene binds more strongly than higher olefins and acrylates.4 The fragment analysis of Table 6 confirms the above conclusions. It can be seen that for the generic system the differences between the catalyst distortion energies in propene and ethene complexes are negligible (13.37 and 11.64 for propene vs 13.21 and 11.55 for ethene), but for the propene complexes the catalyst distortion energy increases more significantly with the increase of the substituents size than for ethene (e.g., 14.72 and 17.62 vs 13.32 and 16.94 in the systems 4g, 4′g vs 2g, 2′g; and 13.77 and 15.94 vs 10.65 and 13.00 in the systems 4i, 4′i vs 2i, 2′i). Finally, it should be noticed that while the steric effects are reflected mainly in the ∆Eg contribution, the bonding energies of distorted reactants (∆Eb) are larger for propene than for ethene for all the catalyst models and for both alkyls. This reflects the electronic preference of propene complexes present in all the systems. A comparison of our results with those obtained from QM/MM approaches for ethylene complexes with catalyst f and its Ni-based analogue shows that these methods lead to similar conlusions:11,15 the π-complex stabilization energy is substantially decreased in the real system in comparison to the generic catalyst. Here, the steric influence is more pronounced than in the case of alkyl β-agostic complexes, so the QM/MM methodology gives correct predictions. D. Olefin Insertion Barriers; 1,2- vs 2,1-Propene Insertion. The ethene and propene insertion barriers are listed in Table 7. The results show that the ethene insertion barriers are not strongly affected by the catalyst substituents; the same is true for the 1,2insertion of propene. The insertion barriers of Table 7 have been calculated with respect to the corresponding olefin π-complexes; therefore, they somehow reflect the trends observed in Table 5. This is especially pronounced in the system g, which has a low insertion barrier and a modest π-complexation energy. One can see the electronic influence from the backbone substituents (R) in the case of the systems e and h, where the barriers are significantly higher than for the generic system a. This effect is more visible here than in the case of π-complex stabilization energies. It is not surprising that the aryl substituents do not affect transition state energies very much in the case of ethene and propene 1,2-insertion. In the transition state geometry the atoms involved in the reaction are situated in the N-Pd-N coordination plane (see Figure



Table 6. Fragment Analysisa of Olefin π-Complex Stabilization Energiesb relative energiesc catalyst R

primary alkyl Ar

∆Eg (∆Eo, ∆Ec)

secondary alkyl ∆Eb



2a 2b 2c 2d 2e 2f 2g 2h 2i

Ethene Complexes 16.80 (3.59,13.21) -35.62 17.42 (4.16, 13.26) -35.17 14.71 (4.07, 10.64) -34.43 14.99 (3.99, 11.00) -33.90 16.37 (3.44, 12.93) -35.23 14.88 (3.79, 11.09) -34.59 17.12 (3.80, 13.32) -33.56 16.27 (3.65, 12.62) -35.64 14.36 (3.71, 10.65) -33.50



4a 4b 4c 4d 4e 4f 4g 4h 4i

Propene Complexes 17.82 (4.45, 13.37) -38.67 18.70 (5.10, 13.60) -38.39 16.18 (4.87, 11.31) -37.43 16.18 (4.93, 11.25) -36.66 17.17 (4.28, 13.42) -37.92 16.37 (4.60, 11.68) -37.25 19.33 (4.61, 14.72) -35.67 17.10 (4.63, 12.47) -38.13 18.08 (4.31, 13.77) -34.90

∆Eg (∆Eo, ∆Ec)

∆Eb

2′a 2′b 2′c 2′d 2′e 2′f 2′g 2′h 2i

15.16 (3.61, 11.55) 18.39 (4.27, 14.12) 15.86 (4.12, 11.74) 16.86 (4.04, 12.82) 15.52 (3.70, 11.82) 17.19 (3.87, 13.32) 20.92 (3.98, 16.94) 14.47 (3.83, 10.64) 16.91 (3.91, 13.00)

-33.34 -32.07 -31.75 -31.32 -33.32 -32.19 -31.73 -33.43 -31.40

4′a 4′b 4′c 4′d 4′e 4′f 4′g 4′h 4′i

16.05 (4.41, 11.64) 19.37 (5.24, 14.13) 17.14 (4.76, 12.38) 17.95 (5.01, 12.94) 16.16 (4.28, 11.88) 18.47 (4.72, 13.75) 22.47 (4.85, 17.62) 15.50 (4.63, 10.87) 20.44 (4.50, 15.94)

-36.13 -34.60 -34.00 -33.73 -35.64 -34.44 -33.15 -35.80 -32.67

a According to eq 1. b Analysis of data from Table 5. c With respect to the energies of isolated reactants, i.e., free olefin and alkyl β-agostic complexes; in kcal/mol.

Table 7. Olefin Insertion Barriers relative energiesa catalyst

a

x

R

Ar

ethene E(3x) - E(2x)

a b c d e f g h i



18.83 19.70 19.62 18.93 19.73 19.26 16.69 20.32 18.90

propene 1,2-ins. E(5x) - E(4x)

propene 2,1-ins. E(6x) - E(4x)

propene ∆E(2,1-2,1) ) E(6x) - E(5x)

22.72 23.38 22.28 21.85 23.18 21.58 18.30 23.59 17.48

20.67 22.99 20.99 20.05 21.42 19.92 18.83 22.31 16.90

-2.05 -0.39 -1.29 -1.80 -1.77 -1.66 +0.53 -1.28 -0.58

With respect to the energies of olefin π-complexes; in kcal/mol.

3c), so there is practically no additional steric repulsion when the size of the substituents is increased. In fact, from a comparison of the results for the systems a, b, c, and d, one can see that the barrier is substantially increased for the catalyst b, with unsubstituted phenyl rings, even though the π-complex stabilization energy is the lowest in this case (see Table 5). This is due to the fact that the unsubstituted phenyl rings in these system adopt an orientation with the phenyl rings close to the N-Pd-N coordination plane (φ1,φ2 , 90°), introducing a repulsion between diimine ligand and olefin in the TS geometry. In the more complex systems (c, d, f, g, i) the intracatalyst repulsions between backbone and aryl substituents (discussed in section A, see Figure 2a) enforce the ring orientation very close to perpendicular, and the size of aryl substituents has no significant influence on the atoms involved in bond breaking/bond formation processes. Since the presence of bulky substituents has no significant influence on the transition states for the ethylene insertion, the QM/MM methods lead to similar predictions11,15 for the system with catalyst f and the corresponding Ni-based complex: the insertion barriers are lowered due to a destabilization of the ethylene π-complex.

Although in the ethene and propene 1,2-insertion the steric effect of the aryl substituents is not significant, it has a strong influence on the 2,1-propene insertion barriers. There is a steric repulsion between the propene methyl and an aryl substituent in the transition state, as illustrated in Figure 3c. This interaction is further seen to increase with the size of the steric bulk on the aryl ring. In the last column of Table 7 we have collected the differences between the 2,1and 1,2-propene insertion barriers. In the generic system (a) the 2,1-insertion is preferred over the 1,2insertion by 2 kcal/mol, for all the real systems this preference is decreased, and eventually, in the most “crowded” systems g and i the barriers differ only by 0.5 kcal/mol, with the 1,2-insertion being preferred for the catalyst g. E. Implications for Polymer Branching. In the previous paper8 we identified the three most important factors controlling the polyolefin branching as the relative stability of isomer alkyl complexes, the relative stability of isomer olefin complexes, and, in the case of propene and higher R-olefins, the 2,1- to 1,2-insertion ratio. Here we have shown that all of them are strongly affected by the diimine substituents. In the generic system (a) branched alkyl complexes, olefin π-complexes

1858


with a branched alkyl, and the 2,1-regioselectivity of insertion are preferred. In the real systems an enhanced preference of the secondary β-agostic alkyl complexes is observed. Thus, the chain straightening isomerization reaction leads to even less stable product in the case of catalysts with large aryl substituents. At the same time, however, the olefin π-complexes with a linear chain become more preferred and more strongly stabilized. Since the resting state of the catalyst is an olefin π-complex,1 this factor is very important. That is, even though the chain straightening isomerization reaction leads to the less stable isomer, afterward the more stable olefin π-complex can be formed. As shown in Scheme 1, the chain straightening isomerization reaction is possible only after 2,1-olefin insertion; a branch introduced by 1,2-insertion cannot be removed, so regioselectivity of the olefin insertion has direct implications for polymer branching. We have demonstrated here that the strong preference of the 2,1insertion in a generic system has been weakened in the real systems; for the largest systems, g and i, the probabilities of both insertions are quite similar, with an energy difference of roughly 0.5 kcal/mol for the barriers. Concluding Remarks We have carried out a DFT study on the cationic Pd(II)-diimine olefin polymerization catalyst due to Brookhart et al.1-3 The objective has been to analyze how diimine ligands with different substituents (i.e., with different electronic and steric properties) influence the relative stabilities of the isomeric alkyl complexes (n- and isopropyl) and the different olefin π-complexes with n- and isopropyl alkyl, as well as the insertion barriers for ethene and propene insertion. The substituent effects were modeled with different combinations of backbone (R ) H, CH3, An) and aryl groups (Ar ) H, -C6H5, -2,6-C6H3(Me)2, -2,6-C6H3(iPr)2). In comparison with the generic diimine ligand (a, R ) H, Ar ) H) we observe a strong substituent effect in the real systems (R ) H, CH3, An; Ar > H). For alkyl complexes, a preference of the system with a branched


alkyl over its linear isomer is enhanced as a result of alkyl-Pd bond (Pd-C and Pd-H) weakening. For olefin π-complexes, the relative stability of isomers is reversed, with the complex involving a linear alkyl becoming preferred over that with a branched alkyl. As a result of the above, the difference in olefin π-complex stabilization energies between the systems with primary and secondary alkyls is substantially increased. Also, the electronic preference of propene π-complexes over those of ethene is overridden by steric factors; for the largest catalysts the ethene complexes become more strongly stabilized, in agreement with experimental results. Finally, for the insertion of propene, the 2,1-regioselectivity becomes less favored; for the largest catalyst modeled the 1,2-insertion has a lower barrier. The above conclusions have direct implications for polyolefin branching. Thus, with the increase in the steric bulk of the diimine substituents the chain straightening isomerization reaction itself becomes less favorable. However, the olefin π-complex with a linear alkyl chain is stabilized more strongly. Finally, at the same time the 1,2-insertion introducing an irremovable branch becomes more facile. The results of the present studies will be used in simulations of polymer chain growth and isomerization, to more quantitatively understand the relationship between the microstructure of the polymer and the structure of the catalyst, as well as the reaction conditions. Acknowledgment. This work has been supported by the National Sciences and Engineering Research Council of Canada (NSERC), as well as by the donors of the Petroleum Research Fund, administered by the American Chemical Society (ACS-PRF No 31205-AC3). A.M. acknowledges the University of Calgary Postdoctoral Fellowship. Supporting Information Available: The optimized geometries of all the structures studied (Cartesian coordinates, in A). This material is available free of charge via the Internet at http://pubs.acs.org. OM990910T

DFT Studies on Substituent Effects in Palladium-Catalyzed Olefin

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